Deck 9: Hypothesis Tests

Question 1

The sum of the values of $\alpha$ and $\beta$

A)always add up to 1.0
B)always add up to 0.5
C)is the probability of Type II error
D)none of these alternatives is correct

Answer 1

none of these alternatives is correct

Question 2

In hypothesis testing, the tentative assumption about the population parameter is

A)the alternative hypothesis
B)the null hypothesis
C)either the null or the alternative
D)None of these alternatives is correct.

Answer 2

the null hypothesis

Question 3

A Type II error is committed when

A)a true alternative hypothesis is mistakenly rejected
B)a true null hypothesis is mistakenly rejected
C)the sample size has been too small
D)not enough information has been available

Answer 3

a true alternative hypothesis is mistakenly rejected

Question 4

For a lower tail test, the p-value is the probability of obtaining a value for the test statistic

A)at least as small as that provided by the sample
B)at least as large as that provided by the sample
C)at least as small as that provided by the population
D)at least as large as that provided by the population.

Question 5

The error of rejecting a true null hypothesis is

A)a Type I error
B)a Type II error
C)is the same as $\beta$
D)committed when not enough information is available

Question 6

In hypothesis testing,

A)the smaller the Type I error, the smaller the Type II error will be
B)the smaller the Type I error, the larger the Type II error will be
C)Type II error will not be effected by Type I error
D)the sum of Type I and Ttype II errors must equal to 1

Question 7

The p-value is a probability that measures the support (or lack of support) for the

A)null hypothesis
B)alternative hypothesis
C)either the null or the alternative hypothesis
D)sample statistic

Question 8

The critical value of t for a two tail test with 6 degrees of freedom is

A)2.447
B)1.943
C)2.365
D)1.985

Question 9

The p-value

A)is the same as the Z statistic
B)measures the number of standard deviations from the mean
C)is a distance
D)is a probability

Question 10

What type of error occurs if you fail to reject H₀ when, in fact, it is not true?

A)Type II
B)Type I
C)either Type I or Type II, depending on the level of significance
D)either Type I or Type II, depending on whether the test is one tail or two tail

Question 11

The level of significance is the

A)maximum allowable probability of Type II error
B)maximum allowable probability of Type I error
C)same as the confidence coefficient
D)same as the p-value

Question 12

We are interested in conducting a study in order to determine what percentage of voters in a city would vote for the incumbent mayor. What is the minimum size sample needed to estimate the population proportion with a margin of error not exceeding 4% at 95% confidence?

A)625
B)626
C)600
D)601

Question 13

The power curve provides the probability of

A)correctly accepting the null hypothesis
B)incorrectly accepting the null hypothesis
C)correctly rejecting the alternative hypothesis
D)correctly rejecting the null hypothesis

Question 14

The p-value

A)can be any value
B)can be any positive value
C)can be any value, negative or positive
D)must be a number between zero and 1

Question 15

An assumption made about the value of a population parameter is called a

A)hypothesis
B)conclusion
C)confidence
D)significance

Question 16

In hypothesis testing if the null hypothesis is rejected,

A)no conclusions can be drawn from the test
B)the alternative hypothesis is true
C)the data must have been accumulated incorrectly
D)the sample size has been too small

Question 17

The level of significance in hypothesis testing is the probability of

A)accepting a true null hypothesis
B)accepting a false null hypothesis
C)rejecting a true null hypothesis
D)None of these alternatives is correct.

Question 18

The probability of committing a Type I error when the null hypothesis is true is

A)the confidence level
B) $\beta$
C)greater than 1
D)the Level of Significance

Question 19

For a two-tail test, the p-value is the probability of obtaining a value for the test statistic as

A)likely as that provided by the sample
B)unlikely as that provided by the sample
C)likely as that provided by the population
D)unlikely as that provided by the population

Question 20

It is known that the population variance ( $\sigma$ ²) is 144. At 95% confidence, what size sample should be taken so that the margin of error is does not exceed 5 or less?

A)22
B)23
C)24
D)25

Question 21

The level of significance

A)can be any positive value
B)can be any value
C)is (1 - confidence level)
D)can be any value between -1.96 to 1.96

Question 22

In order to test the following hypotheses at an $\alpha$ level of significance H₀: $\mu$ 800
H_a: $\mu$ > 800
The null hypothesis will be rejected if the test statistic Z is

A) Z _$\alpha$
B)< Z _$\alpha$
C)< -Z _$\alpha$
D)= $\alpha$

Question 23

When the p-value is used for hypothesis testing, the null hypothesis is rejected if

A)p-value $\alpha$
B) $\alpha$ < p-value
C)p-value $\alpha$
D)p-value = 1 - $\alpha$

Question 24

When the following hypotheses are being tested at a level of significance of $\alpha$ H₀: $\mu$ 500
H_a: $\mu$ < 500
The null hypothesis will be rejected if the p-value is

A) $\alpha$
B)> $\alpha$
C)> $\alpha$ /2
D) 1 - $\alpha$ /2

Question 25

If a hypothesis is rejected at 95% confidence, it

A)will always be accepted at 90% confidence
B)will always be rejected at 90% confidence
C)will sometimes be rejected at 90% confidence
D)None of these alternatives is correct.

Question 26

In the hypothesis testing procedure, $\alpha$ is

A)the level of significance
B)the critical value
C)the confidence level
D)1 - level of significance

Question 27

As the test statistic becomes larger, the p-value

A)gets smaller
B)becomes larger
C)stays the same, since the sample size has not been changed
D)becomes negative

Question 28

If a hypothesis test leads to the rejection of the null hypothesis,

A)a Type II error must have been committed
B)a Type II error may have been committed
C)a Type I error must have been committed
D)a Type I error may have been committed

Question 29

If a hypothesis is rejected at the 5% level of significance, it

A)will always be rejected at the 1% level
B)will always be accepted at the 1% level
C)will never be tested at the 1% level
D)may be rejected or not rejected at the 1% level

Question 30

The probability of making a Type I error is denoted by

A) $\alpha$
B) $\beta$
C)1 - $\alpha$
D)1 - $\beta$

Question 31

The p-value ranges between

A)zero and infinity
B)minus infinity to plus infinity
C)zero to one
D)-1 to +1

Question 32

Which of the following does not need to be known in order to compute the p-value?

A)knowledge of whether the test is one-tailed or two-tailed
B)the value of the test statistic
C)the level of significance
D)None of these alternatives is correct.

Question 33

If the level of significance of a hypothesis test is raised from .01 to .05, the probability of a Type II error

A)will also increase from .01 to .05
B)will not change
C)will decrease
D)will increase

Question 34

For a lower bounds one-tailed test, the test statistic z is determined to be zero. The p-value for this test is

A)zero
B)-0.5
C)+0.5
D)1.00

Question 35

In hypothesis testing if the null hypothesis has been rejected when the alternative hypothesis has been true,

A)a Type I error has been committed
B)a Type II error has been committed
C)either a Type I or Type II error has been committed
D)the correct decision has been made

Question 36

In a two-tailed hypothesis test situation, the test statistic is determined to be t = -2.692. The sample size has been 45. The p-value for this test is

A)-0.005
B)+0.005
C)-0.01
D)+0.01

Question 37

In a lower one-tail hypothesis test situation, the p-value is determined to be 0.2. If the sample size for this test is 51, the t statistic has a value of

A)0.849
B)-0.849
C)1.299
D)-1.299

Question 38

The probability of making a Type II error is denoted by

A) $\alpha$
B) $\beta$
C)1 - $\alpha$
D)1 - $\beta$

Question 39

If the probability of a Type I error ( $\alpha$ ) is 0.05, then the probability of a Type II error ( $\beta$ ) must be

A)0.05
B)0.95
C)0.025
D)None of these alternatives is correct.

Question 40

If a hypothesis is not rejected at the 5% level of significance, it

A)will also not be rejected at the 1% level
B)will always be rejected at the 1% level
C)will sometimes be rejected at the 1% level
D)None of these alternatives is correct.

Question 41

Read the Z statistic from the normal distribution table and circle the correct answer. A one-tailed test (upper tail) at 87.7% confidence; Z =

A)1.54
B)1.96
C)1.645
D)1.16

Question 42

A machine is designed to fill toothpaste tubes with 5.8 ounces of toothpaste. The manufacturer does not want any underfilling or overfilling. The correct hypotheses to be tested are

A)
B)
C)
D)

Question 43

A two-tailed test is performed at 95% confidence. The p-value is determined to be 0.09. The null hypothesis

A)must be rejected
B)should not be rejected
C)could be rejected, depending on the sample size
D)has been designed incorrectly

Question 44

In a one-tailed hypothesis test (lower tail) the test statistic is determined to be -2. The p-value for this test is

A)0.4772
B)0.0228
C)0.0056
D)0.5228

Question 45

For a one-tailed test (upper tail), a sample size of 26 at 90% confidence, t =

A)1.316
B)-1.316
C)-1.740
D)1.740

Question 46

For a one-tailed test (lower tail), a sample size of 10 at 90% confidence, t =

A)1.383
B)2.821
C)-1.383
D)-2.821

Question 47

For a one-tailed test (lower tail) at 93.7% confidence, Z =

A)-1.86
B)-1.53
C)-1.96
D)-1.645

Question 48

The average manufacturing work week in metropolitan Chattanooga was 40.1 hours last year. It is believed that the recession has led to a reduction in the average work week. To test the validity of this belief, the hypotheses are

A)
B)
C)
D)

Question 49

The average hourly wage of computer programmers with 2 years of experience has been $21.80. Because of high demand for computer programmers, it is believed there has been a significant increase in the average wage of computer programmers. To test whether or not there has been an increase, the correct hypotheses to be tested are

A)
B)
C)
D)

Question 50

The average monthly rent for one-bedroom apartments in Chattanooga has been $700. Because of the downturn in the real estate market, it is believed that there has been a decrease in the average rental. The correct hypotheses to be tested are

A)
B)
C)
D)

Question 51

For a two-tailed test at 98.4% confidence, Z =

A)1.96
B)1.14
C)2.41
D)0.8612

Question 52

A student believes that the average grade on the final examination in statistics is at least 85. She plans on taking a sample to test her belief. The correct set of hypotheses is

A)H₀: $\mu$ < 85 H_a: $\mu$ 85
B)H₀: $\mu$ 85 H_a: $\mu$ > 85
C)H₀: $\mu$ 85 H_a: $\mu$ < 85
D)H₀: $\mu$ > 85 H_a: $\mu$ 85

Question 53

For a one-tailed test (upper tail), a sample size of 18 at 95% confidence, t =

A)2.12
B)-2.12
C)-1.740
D)1.740

Question 54

For a one-tailed test (lower tail) at 89.8% confidence, Z =

A)-1.27
B)-1.53
C)-1.96
D)-1.64

Question 55

For a two-tailed test at 86.12% confidence, Z =

A)1.96
B)1.48
C)1.09
D)0.86

Question 56

For a one-tailed test (upper tail) at 93.7% confidence, Z =

A)1.50
B)1.96
C)1.645
D)1.53

Question 57

In a two-tailed hypothesis test the test statistic is determined to be Z = -2.5. The p-value for this test is

A)-1.25
B)0.4938
C)0.0062
D)0.0124

Question 58

For a one-tailed test (lower tail) with 22 degrees of freedom at 95% confidence, the value of t =

A)-1.383
B)1.383
C)-1.717
D)-1.721

Question 59

For a one-tailed hypothesis test (upper tail) the p-value is computed to be 0.034. If the test is being conducted at 95% confidence, the null hypothesis

A)could be rejected or not rejected depending on the sample size
B)could be rejected or not rejected depending on the value of the mean of the sample
C)is not rejected
D)is rejected

Question 60

For a two-tailed test, a sample of 20 at 80% confidence, t =

A)1.328
B)2.539
C)1.325
D)2.528

Question 61

In the past, 75% of the tourists who visited Chattanooga went to see Rock City. The management of Rock City recently undertook an extensive promotional campaign. They are interested in determining whether the promotional campaign actually increased the proportion of tourists visiting Rock City. The correct set of hypotheses is

A)H₀: P > 0.75 H_a: P 0.75
B)H₀: P < 0.75 H_a: P 0.75
C)H₀: P 0.75 H_a: P < 0.75
D)H₀: P 0.75 H_a: P > 0.75

Question 62

Exhibit 9-2
n = 64 = 50
s = 16
H₀: $\mu$ 54
H_a: $\mu$ < 54

-Refer to Exhibit 9-2. If the test is done at 95% confidence, the null hypothesis should

A)not be rejected
B)be rejected
C)Not enough information is given to answer this question.
D)None of these alternatives is correct.

Question 63

The manager of an automobile dealership is considering a new bonus plan in order to increase sales. Currently, the mean sales rate per salesperson is five automobiles per month. The correct set of hypotheses for testing the effect of the bonus plan is

A)H₀: $\mu$ < 5 H_a: $\mu$ 5
B)H₀: $\mu$ 5 H_a: $\mu$ > 5
C)H₀: $\mu$ > 5 H_a: $\mu$ 5
D)H₀: $\mu$ 5 H_a: $\mu$ < 5

Question 64

Exhibit 9-3
n = 49 = 54.8
s = 28
H₀: $\mu$ 50
H_a: $\mu$ > 50

-Refer to Exhibit 9-3. If the test is done at the 5% level of significance, the null hypothesis should

A)not be rejected
B)be rejected
C)Not enough information given to answer this question.
D)None of these alternatives is correct.

Question 65

Your investment executive claims that the average yearly rate of return on the stocks she recommends is at least 10.0%. You plan on taking a sample to test her claim. The correct set of hypotheses is

A)H₀: $\mu$ < 10.0% H_a: $\mu$ 10.0%
B)H₀: $\mu$ 10.0% H_a: $\mu$ > 10.0%
C)H₀: $\mu$ > 10.0% H_a: $\mu$ 10.0%
D)H₀: $\mu$ 10.0% H_a: $\mu$ < 10.0%

Question 66

A sample of 1400 items had 280 defective items. For the following hypothesis test, H_o: P = 0.20
H_a: P > 0.20
The test statistic is

A)0.28
B)0.14
C)28%
D)zero

Question 67

A weatherman stated that the average temperature during July in Chattanooga is 80 degrees or less. A sample of 32 Julys is taken. The correct set of hypotheses is

A)H₀: $\mu$ 80 H_a: $\mu$ < 80
B)H₀: $\mu$ 80 H_a: $\mu$ > 80
C)H₀: $\mu$ $\neq$ 80 H_a: $\mu$ = 80
D)H₀: $\mu$ < 80 H_a: $\mu$ > 80

Question 68

Exhibit 9-3
n = 49 = 54.8
s = 28
H₀: $\mu$ 50
H_a: $\mu$ > 50

-Refer to Exhibit 9-3. The p-value is between

A)0.01 to 0.025
B)0.025 to 0.05
C).05 to 0.1
D)0.1 to 0.2

Question 69

The school's newspaper reported that the proportion of students majoring in business is at least 30%. You plan on taking a sample to test the newspaper's claim. The correct set of hypotheses is

A)H₀: P < 0.30 H_a: P 0.30
B)H₀: P 0.30 H_a: P > 0.30
C)H₀: P 0.30 H_a: P < 0.30
D)H₀: P > 0.30 H_a: P 0.30

Question 70

The academic planner of a university thinks that at least 35% of the entire student body attends summer school. The correct set of hypotheses to test his belief is

A)H₀: P > 0.35 H_a: P 0.35
B)H₀: P 0.35 H_a: P > 0.35
C)H₀: P 0.35 H_a: P < 0.35
D)H₀: P > 0.35 H_a: P 0.35

Question 71

Exhibit 9-3
n = 49 = 54.8
s = 28
H₀: $\mu$ 50
H_a: $\mu$ > 50

-Refer to Exhibit 9-3. The test statistic is

A)0.1714
B)0.3849
C)-1.2
D)1.2

Question 72

Given the following information, the test statistic is n = 49 = 50 S = 7 H_o: $\mu$ > 52
H_a: $\mu$ < 52
The test statistic for the above information is

A)2
B)-2
C)1
D)-1

Question 73

Exhibit 9-2
n = 64 = 50
s = 16
H₀: $\mu$ 54
H_a: $\mu$ < 54

-Refer to Exhibit 9-2. The test statistic equals

A)-4
B)-3
C)-2
D)-1

Question 74

A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. Any over filling or under filling results in the shutdown and readjustment of the machine. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is

A)H₀: $\mu$ < 12 H_a: $\mu$ 12
B)H₀: $\mu$ 12 H_a: $\mu$ > 12
C)H₀: $\mu$$\neq$ 12 H_a: $\mu$ = 12
D)H₀: $\mu$ = 12 H_a: $\mu$$\neq$ 12

Question 75

Exhibit 9-1
n = 36 = 24.6
S = 12
H₀: $\mu$ 20
H_a: $\mu$ > 20

-Refer to Exhibit 9-1. If the test is done at 95% confidence, the null hypothesis should

A)not be rejected
B)be rejected
C)Not enough information is given to answer this question.
D)None of these alternatives is correct.

Question 76

The average life expectancy of tires produced by the Whitney Tire Company has been 40,000 miles. Management believes that due to a new production process, the life expectancy of their tires has increased. In order to test the validity of their belief, the correct set of hypotheses is

A)H₀: $\mu$ < 40,000 H_a: $\mu$ 40,000
B)H₀: $\mu$ 40,000 H_a: $\mu$ > 40,000
C)H₀: $\mu$ > 40,000 H_a: $\mu$ 40,000
D)H₀: $\mu$ 40,000 H_a: $\mu$ < 40,000

Question 77

Exhibit 9-2
n = 64 = 50
s = 16
H₀: $\mu$ 54
H_a: $\mu$ < 54

-Refer to Exhibit 9-2. The p-value is between

A).005 to .01
B).01 to .025
C).025 to .05
D).05 to .01

Question 78

Exhibit 9-1
n = 36 = 24.6
S = 12
H₀: $\mu$ 20
H_a: $\mu$ > 20

-Refer to Exhibit 9-1. The p-value is between

A)0.005 to 0.01
B)0.01 to 0.025
C)0.025 to 0.05
D)0.05 to 0.10

Question 79

For the following hypothesis test, H_o: $\mu$ = 150
H_a: $\mu$ < 150
The test statistic

A)must be negative
B)must be positive
C)can be either negative or positive
D)must be a number between zero and 1

Question 80

Exhibit 9-1
n = 36 = 24.6
S = 12
H₀: $\mu$ 20
H_a: $\mu$ > 20

-Refer to Exhibit 9-1. The test statistic is

A)2.3
B)0.38
C)-2.3
D)-0.38